The problem is Murtough is in charge now, say even if he gets replaced halfway through this season, the new DOF is going to have to come in and start from scratch rebuilding the footballing structure at the club if Murtough has failed to do this.
One of the main things the supporters of Murtough say is that he has only really been a proper DOF since Woodward left, before that he was only DOF by name alone(which for me raises all kinds of questions regarding his competency for the job). But anyway IF its true that Murtough has only really been doing the job 6 months, and that isn't enough time to get the recruitment structure in place which is why we are so heavily manager lead recruitment this summer. Now obviously we have no idea how much this is true and how much is speculation/ wishful thinking, but surely a new DOF would require the same time at least as people are saying Murtough needs.
So if Murtough isn't the right man for the job, then it will be at the very very earliest around the summer of 2024 and god knows how many millions spent before we even start to see the impact of a different DOF and that's if they were employed this season. So personally I would say that is very much up a certain brown alley if Murtough doesn't come through.